4-4-4 
routes of the digital road network in the environment of the 
vehicle position. The most appropriate route a vehicle has used 
and so the position to be found relatively to the digital map by 
techniques of pattern recognition and image matching as used in 
photogrammetry. The measurement model of such a system is 
shown in picture 2. 
This type of positioning is named map matching in the literature 
due to the fact that the driven route has to be matched with the 
map continuously during the driving process. Due to magnetic 
disturbances wheel slips and gaps in digitalization of the road 
network the loss of position up to a total system failure was 
recorded in the past. 
This system disadvantage can be explained if we interpret the 
measurement of changes in heading versus changes in distance. 
This value is known as curvature k in differential geometry. The 
curvature Kis a motion and parameter invariance scalar so-called 
natural invariant of plain curves and describes a coordinate 
system independent formula for the curve. Solution strategies 
based on measured curvature patterns in comparison to the cur 
vature pattern of a digital road map can be used by pattern recog 
nition techniques compared with square computation methods. 
Prerequisite is the availability of 3 significant curvature signals 
for reliable map matching processes. Practical measurements and 
computations have shown the high performance of this technique 
based on digital road maps with an accuracy of 10-15m (RMS). A 
position accuracy of lm relatively to the digitized road network 
can be achieved. In the following the adjustment approach 
described in the performance of the solution is shown with 2 
different examples. 
4 MAP MATCHING WITH CURVATURES 
The measured track has to be matched with the sample of road 
element of the digital map. Due to measurement errors the coor 
dinates of the vehicle position are inaccurate. With an appropriate 
search algorithm all available tracks in the digital map are 
extracted where the car could have moved mutually. For these 
alternate tracks the curvature patterns will be developed and the 
orientation of the road segments are filtered and differentiated. 
The so developed curvature pattern leads towards the reference 
for the map matching process. 
The measured curvature pattern in the vehicle will be compared 
to the different alternating route tracks and the RMS of the 
adjustment result will be used to select the most appropriate track 
from the digital map. 
Picture 4: Measured and computed curvature patterns 
For the map matching of 2 different curvature patterns there are 
different recognition algorithms available. Similarity of 2 
functions can be described by correlation methods and the cross 
correlation can be described by 
c(i) = ]►] a(j) • b(i + j) = a(i) o b(i); 
j=- °° 
where the signals a(i) and b(i) are curvatures(x,) and K 2 (y t ) 
in the appropriate picture. This method provides sufficient 
accuracy for the start solution of a nonlinear least square 
adjustment. 
5 MAP MATCHING WITH LEAST SQUARE METHODS 
Basic idea of the transformation between curvature profiles 
/c,(x,) and. ic 2 (y i ) are 
- translation u b and scale factor m b between the distance 
y, = m b *x i -u b 
- translation b and scale factor a between measured curvature 
and computed curvature of the digital map 
tc l (x i ) = a*K 2 (y i ) + b + n(x ) 
For the adjustment the following functional model is chosen 
K x (x i ) = a*K 1 (m h x i -u b ) + b + n(x i ) 
and the nonlinear observable equation 
K ï (x l ) + V(x l ) = a* f(y,) + b-, 
This observable equation is heavily nonlinear and requires solu 
tion in a, m b and u b .